ThisvolumeoftheLectureNotesinComputerScienceseriescontainsthep- ceedings of the Second Conference on Numerical Analysis and Applications, which was held at the University of Rousse, Bulgaria, June 11-15,2000. The conferencewasorganizedbytheDepartmentofNumericalAnalysisandStat- ticsattheUniversityofRoussewithsupportfromtheUniversityofSouthern Mississippi, Hattiesburg. The conference was co-sponsored by SIAM (Society for Industrial and Applied Mathematics) and ILAS (International Linear - gebra Society). The o?cial sponsors of the conference were Fujitsu America, Inc. ,Hewlett-PackardGmbH,andSunMicrosystems. Wewouldliketogiveour sincerethankstoallsponsorsandco-sponsorsforthetimelysupport. The second conference continued the tradition of the ?rst one (1996 in Rousse) as a forum, where scientists from leading research groups from the "East" and "West" are provided with the opportunity to meet and exchange ideasandestablishresearchcooperation. Morethan120scientistsfrom31co- triesparticipatedintheconference. Awiderangeofproblemsconcerningrecentachievementsinnumericalan- ysisanditsapplicationsinphysics,chemistry,engineering,andeconomicswere discussed.An extensiveexchangeofideasbetweenscientists whodevelopand studynumericalmethodsandresearcherswhousethemforsolvingreal-lifepr- lemstookplaceduringtheconference. Weareindebtedtoourcolleagueswhohelpedusintheorganizationofthis conference. Wethanktheorganizersofthemini-symposiaforattractingactive andhighlyquali?edresearchers. October2000 LubinVulkov JerzyWa'sniewski PlamenYalamov Table of Contents Numerical Analysis and Its Applications SensitivityAnalysisoftheExpectedAccumulatedReward UsingUniformizationandIRK3Methods ...1 H. Abdallah andM. Hamza SpectralPropertiesofCirculantBandMatricesArisinginODEMethods ...10 P. Amodio AParameterRobustMethodforaProblemwith aSymmetryBoundaryLayer ...18 A. R. Ansari,A. F. HegartyandG. I. Shishkin AnAlgorithmBasedonOrthogonalPolynomialVectors forToeplitzLeastSquaresProblems ...27 M. VanBarel, G. Heinig andP. Kravanja FromSensitivityAnalysistoRandomFloatingPointArithmetics- ApplicationtoSylvesterEquations...35 A. Barraud, S. LesecqandN. Christov ConstructionofSeminumericalSchemes: ApplicationtotheArti?cialSatelliteProblem ...42 R. Barrio StabilityAnalysisofParallelEvaluationofFiniteSeries ofOrthogonalPolynomials ...51 R. Barrio andP.Yalamov OnSolvingLarge-ScaleWeightedLeastSquaresProblems...59 V. Baryamureeba AHybridNewton-GMRESMethodforSolvingNonlinearEquations ...68 S. Bellavia, M. Macconi andB. Morini ComparativeAnalysisofMarchingAlgorithms forSeparableEllipticProblems ...76 G. Bencheva InexactNewtonMethodsandMixedNonlinearComplementaryProblems . . 84 L. Bergamaschi and G. Zilli Skew-CirculantPreconditionersforSystemsofLMF-BasedODECodes ...93 D. Bertaccini andM. K. Ng NewFamiliesofSymplecticRunge-Kutta-NystromIntegrationMethods . . 102 S. Blanes, F. Casas andJ. Ros VIII Table ofContents ConvergenceofFiniteDi?erenceMethodforParabolicProblem withVariableOperator...110 D. Bojovi' c FiniteVolumeDi?erenceSchemefor aSti?EllipticReaction-Di?usionProblemwithaLineInterface ...117 I. A. Braianov Nested-DissectionOrderingsforSparseLUwithPartialPivoting...125 I. Brainman andS. Toledo FractionalStepRunge-ThisvolumeoftheLectureNotesinComputerScienceseriescontainsthep- ceedings of the Second Conference on Numerical Analysis and Applications, which was held at the University of Rousse, Bulgaria, June 11-15,2000.The conferencewasorganizedbytheDepartmentofNumericalAnalysisandStat- ticsattheUniversityofRoussewithsupportfromtheUniversityofSouthern Mississippi, Hattiesburg. The conference was co-sponsored by SIAM (Society for Industrial and Applied Mathematics) and ILAS (International Linear - gebra Society). The o?cial sponsors of the conference were Fujitsu America, Inc. ,Hewlett-PackardGmbH,andSunMicrosystems. Wewouldliketogiveour sincerethankstoallsponsorsandco-sponsorsforthetimelysupport. The second conference continued the tradition of the ?rst one (1996 in Rousse) as a forum, where scientists from leading research groups from the "East" and "West" are provided with the opportunity to meet and exchange ideasandestablishresearchcooperation. Morethan120scientistsfrom31co- triesparticipatedintheconference. Awiderangeofproblemsconcerningrecentachievementsinnumericalan- ysisanditsapplicationsinphysics,chemistry,engineering,andeconomicswere discussed. An extensiveexchangeofideasbetweenscientists whodevelopand studynumericalmethodsandresearcherswhousethemforsolvingreal-lifepr- lemstookplaceduringtheconference. Weareindebtedtoourcolleagueswhohelpedusintheorganizationofthis conference.Wethanktheorganizersofthemini-symposiaforattractingactive andhighlyquali?edresearchers. October2000 LubinVulkov JerzyWa'sniewski PlamenYalamov Table of Contents Numerical Analysis and Its Applications SensitivityAnalysisoftheExpectedAccumulatedReward UsingUniformizationandIRK3Methods ...1 H. Abdallah andM. Hamza SpectralPropertiesofCirculantBandMatricesArisinginODEMethods ...10 P. Amodio AParameterRobustMethodforaProblemwith aSymmetryBoundaryLayer ...18 A. R. Ansari,A. F. HegartyandG. I. Shishkin AnAlgorithmBasedonOrthogonalPolynomialVectors forToeplitzLeastSquaresProblems ...27 M. VanBarel, G. Heinig andP. Kravanja FromSensitivityAnalysistoRandomFloatingPointArithmetics- ApplicationtoSylvesterEquations...35 A. Barraud, S. LesecqandN. Christov ConstructionofSeminumericalSchemes: ApplicationtotheArti?cialSatelliteProblem ...42 R. Barrio StabilityAnalysisofParallelEvaluationofFiniteSeries ofOrthogonalPolynomials ...51 R. Barrio andP. Yalamov OnSolvingLarge-ScaleWeightedLeastSquaresProblems...59 V. Baryamureeba AHybridNewton-GMRESMethodforSolvingNonlinearEquations ...68 S. Bellavia, M. Macconi andB. Morini ComparativeAnalysisofMarchingAlgorithms forSeparableEllipticProblems ...76 G.Bencheva InexactNewtonMethodsandMixedNonlinearComplementaryProblems . . 84 L. Bergamaschi and G. Zilli Skew-CirculantPreconditionersforSystemsofLMF-BasedODECodes ...93 D. Bertaccini andM. K. Ng NewFamiliesofSymplecticRunge-Kutta-NystromIntegrationMethods . . 102 S. Blanes, F. Casas andJ. Ros VIII Table ofContents ConvergenceofFiniteDi?erenceMethodforParabolicProblem withVariableOperator...110 D. Bojovi' c FiniteVolumeDi?erenceSchemefor aSti?EllipticReaction-Di?usionProblemwithaLineInterface ...117 I. A. Braianov Nested-DissectionOrderingsforSparseLUwithPartialPivoting...125 I. Brainman andS. Toledo FractionalStepRunge-KuttaMethodsfortheResolutionof TwoDimensionalTimeDependentCoe?cient Convection-Di?usionProblems...133 B. Bujanda andJ. C. Jorge VariableStepsizesinSymmetricLinearMultistepMethods...144 B. Cano PreliminaryRemarksonMultigridMethodsforCirculantMatrices ...

ThisvolumeoftheLectureNotesinComputerScienceseriescontainsthep- ceedings of the Second Conference on Numerical Analysis and Applications, which was held at the University of Rousse, Bulgaria, June 11-15,2000. The conferencewasorganizedbytheDepartmentofNumericalAnalysisandStat- ticsattheUniversityofRoussewithsupportfromtheUniversityofSouthern Mississippi, Hattiesburg. The conference was co-sponsored by SIAM (Society for Industrial and Applied Mathematics) and ILAS (International Linear - gebra Society). The o?cial sponsors of the conference were Fujitsu America, Inc. ,Hewlett-PackardGmbH,andSunMicrosystems. Wewouldliketogiveour sincerethankstoallsponsorsandco-sponsorsforthetimelysupport. The second conference continued the tradition of the ?rst one (1996 in Rousse) as a forum, where scientists from leading research groups from the "East" and "West" are provided with the opportunity to meet and exchange ideasandestablishresearchcooperation. Morethan120scientistsfrom31co- triesparticipatedintheconference. Awiderangeofproblemsconcerningrecentachievementsinnumericalan- ysisanditsapplicationsinphysics,chemistry,engineering,andeconomicswere discussed.An extensiveexchangeofideasbetweenscientists whodevelopand studynumericalmethodsandresearcherswhousethemforsolvingreal-lifepr- lemstookplaceduringtheconference. Weareindebtedtoourcolleagueswhohelpedusintheorganizationofthis conference. Wethanktheorganizersofthemini-symposiaforattractingactive andhighlyquali?edresearchers. October2000 LubinVulkov JerzyWa'sniewski PlamenYalamov Table of Contents Numerical Analysis and Its Applications SensitivityAnalysisoftheExpectedAccumulatedReward UsingUniformizationandIRK3Methods ...1 H. Abdallah andM. Hamza SpectralPropertiesofCirculantBandMatricesArisinginODEMethods ...10 P. Amodio AParameterRobustMethodforaProblemwith aSymmetryBoundaryLayer ...18 A. R. Ansari,A. F. HegartyandG. I. Shishkin AnAlgorithmBasedonOrthogonalPolynomialVectors forToeplitzLeastSquaresProblems ...27 M. VanBarel, G. Heinig andP. Kravanja FromSensitivityAnalysistoRandomFloatingPointArithmetics- ApplicationtoSylvesterEquations...35 A. Barraud, S. LesecqandN. Christov ConstructionofSeminumericalSchemes: ApplicationtotheArti?cialSatelliteProblem ...42 R. Barrio StabilityAnalysisofParallelEvaluationofFiniteSeries ofOrthogonalPolynomials ...51 R. Barrio andP.Yalamov OnSolvingLarge-ScaleWeightedLeastSquaresProblems...59 V. Baryamureeba AHybridNewton-GMRESMethodforSolvingNonlinearEquations ...68 S. Bellavia, M. Macconi andB. Morini ComparativeAnalysisofMarchingAlgorithms forSeparableEllipticProblems ...76 G. Bencheva InexactNewtonMethodsandMixedNonlinearComplementaryProblems . . 84 L. Bergamaschi and G. Zilli Skew-CirculantPreconditionersforSystemsofLMF-BasedODECodes ...93 D. Bertaccini andM. K. Ng NewFamiliesofSymplecticRunge-Kutta-NystromIntegrationMethods . . 102 S. Blanes, F. Casas andJ. Ros VIII Table ofContents ConvergenceofFiniteDi?erenceMethodforParabolicProblem withVariableOperator...110 D. Bojovi' c FiniteVolumeDi?erenceSchemefor aSti?EllipticReaction-Di?usionProblemwithaLineInterface ...117 I. A. Braianov Nested-DissectionOrderingsforSparseLUwithPartialPivoting...125 I. Brainman andS. Toledo FractionalStepRunge-ThisvolumeoftheLectureNotesinComputerScienceseriescontainsthep- ceedings of the Second Conference on Numerical Analysis and Applications, which was held at the University of Rousse, Bulgaria, June 11-15,2000.The conferencewasorganizedbytheDepartmentofNumericalAnalysisandStat- ticsattheUniversityofRoussewithsupportfromtheUniversityofSouthern Mississippi, Hattiesburg. The conference was co-sponsored by SIAM (Society for Industrial and Applied Mathematics) and ILAS (International Linear - gebra Society). The o?cial sponsors of the conference were Fujitsu America, Inc. ,Hewlett-PackardGmbH,andSunMicrosystems. Wewouldliketogiveour sincerethankstoallsponsorsandco-sponsorsforthetimelysupport. The second conference continued the tradition of the ?rst one (1996 in Rousse) as a forum, where scientists from leading research groups from the "East" and "West" are provided with the opportunity to meet and exchange ideasandestablishresearchcooperation. Morethan120scientistsfrom31co- triesparticipatedintheconference. Awiderangeofproblemsconcerningrecentachievementsinnumericalan- ysisanditsapplicationsinphysics,chemistry,engineering,andeconomicswere discussed. An extensiveexchangeofideasbetweenscientists whodevelopand studynumericalmethodsandresearcherswhousethemforsolvingreal-lifepr- lemstookplaceduringtheconference. Weareindebtedtoourcolleagueswhohelpedusintheorganizationofthis conference.Wethanktheorganizersofthemini-symposiaforattractingactive andhighlyquali?edresearchers. October2000 LubinVulkov JerzyWa'sniewski PlamenYalamov Table of Contents Numerical Analysis and Its Applications SensitivityAnalysisoftheExpectedAccumulatedReward UsingUniformizationandIRK3Methods ...1 H. Abdallah andM. Hamza SpectralPropertiesofCirculantBandMatricesArisinginODEMethods ...10 P. Amodio AParameterRobustMethodforaProblemwith aSymmetryBoundaryLayer ...18 A. R. Ansari,A. F. HegartyandG. I. Shishkin AnAlgorithmBasedonOrthogonalPolynomialVectors forToeplitzLeastSquaresProblems ...27 M. VanBarel, G. Heinig andP. Kravanja FromSensitivityAnalysistoRandomFloatingPointArithmetics- ApplicationtoSylvesterEquations...35 A. Barraud, S. LesecqandN. Christov ConstructionofSeminumericalSchemes: ApplicationtotheArti?cialSatelliteProblem ...42 R. Barrio StabilityAnalysisofParallelEvaluationofFiniteSeries ofOrthogonalPolynomials ...51 R. Barrio andP. Yalamov OnSolvingLarge-ScaleWeightedLeastSquaresProblems...59 V. Baryamureeba AHybridNewton-GMRESMethodforSolvingNonlinearEquations ...68 S. Bellavia, M. Macconi andB. Morini ComparativeAnalysisofMarchingAlgorithms forSeparableEllipticProblems ...76 G.Bencheva InexactNewtonMethodsandMixedNonlinearComplementaryProblems . . 84 L. Bergamaschi and G. Zilli Skew-CirculantPreconditionersforSystemsofLMF-BasedODECodes ...93 D. Bertaccini andM. K. Ng NewFamiliesofSymplecticRunge-Kutta-NystromIntegrationMethods . . 102 S. Blanes, F. Casas andJ. Ros VIII Table ofContents ConvergenceofFiniteDi?erenceMethodforParabolicProblem withVariableOperator...110 D. Bojovi' c FiniteVolumeDi?erenceSchemefor aSti?EllipticReaction-Di?usionProblemwithaLineInterface ...117 I. A. Braianov Nested-DissectionOrderingsforSparseLUwithPartialPivoting...125 I. Brainman andS. Toledo FractionalStepRunge-KuttaMethodsfortheResolutionof TwoDimensionalTimeDependentCoe?cient Convection-Di?usionProblems...133 B. Bujanda andJ. C. Jorge VariableStepsizesinSymmetricLinearMultistepMethods...144 B. Cano PreliminaryRemarksonMultigridMethodsforCirculantMatrices ...

ThisvolumeoftheLectureNotesinComputerScienceseriescontainsthep- ceedings of the Second Conference on Numerical Analysis and Applications, which was held at the University of Rousse, Bulgaria, June 11-15,2000. The conferencewasorganizedbytheDepartmentofNumericalAnalysisandStat- ticsattheUniversityofRoussewithsupportfromtheUniversityofSouthern Mississippi, Hattiesburg. The conference was co-sponsored by SIAM (Society for Industrial and Applied Mathematics) and ILAS (International Linear - gebra Society). The o?cial sponsors of the conference were Fujitsu America, Inc. ,Hewlett-PackardGmbH,andSunMicrosystems. Wewouldliketogiveour sincerethankstoallsponsorsandco-sponsorsforthetimelysupport. The second conference continued the tradition of the ?rst one (1996 in Rousse) as a forum, where scientists from leading research groups from the "East" and "West" are provided with the opportunity to meet and exchange ideasandestablishresearchcooperation. Morethan120scientistsfrom31co- triesparticipatedintheconference. Awiderangeofproblemsconcerningrecentachievementsinnumericalan- ysisanditsapplicationsinphysics,chemistry,engineering,andeconomicswere discussed.An extensiveexchangeofideasbetweenscientists whodevelopand studynumericalmethodsandresearcherswhousethemforsolvingreal-lifepr- lemstookplaceduringtheconference. Weareindebtedtoourcolleagueswhohelpedusintheorganizationofthis conference. Wethanktheorganizersofthemini-symposiaforattractingactive andhighlyquali?edresearchers. October2000 LubinVulkov JerzyWa'sniewski PlamenYalamov Table of Contents Numerical Analysis and Its Applications SensitivityAnalysisoftheExpectedAccumulatedReward UsingUniformizationandIRK3Methods ...1 H. Abdallah andM. Hamza SpectralPropertiesofCirculantBandMatricesArisinginODEMethods ...10 P. Amodio AParameterRobustMethodforaProblemwith aSymmetryBoundaryLayer ...18 A. R. Ansari,A. F. HegartyandG. I. Shishkin AnAlgorithmBasedonOrthogonalPolynomialVectors forToeplitzLeastSquaresProblems ...27 M. VanBarel, G. Heinig andP. Kravanja FromSensitivityAnalysistoRandomFloatingPointArithmetics- ApplicationtoSylvesterEquations...35 A. Barraud, S. LesecqandN. Christov ConstructionofSeminumericalSchemes: ApplicationtotheArti?cialSatelliteProblem ...42 R. Barrio StabilityAnalysisofParallelEvaluationofFiniteSeries ofOrthogonalPolynomials ...51 R. Barrio andP.Yalamov OnSolvingLarge-ScaleWeightedLeastSquaresProblems...59 V. Baryamureeba AHybridNewton-GMRESMethodforSolvingNonlinearEquations ...68 S. Bellavia, M. Macconi andB. Morini ComparativeAnalysisofMarchingAlgorithms forSeparableEllipticProblems ...76 G. Bencheva InexactNewtonMethodsandMixedNonlinearComplementaryProblems . . 84 L. Bergamaschi and G. Zilli Skew-CirculantPreconditionersforSystemsofLMF-BasedODECodes ...93 D. Bertaccini andM. K. Ng NewFamiliesofSymplecticRunge-Kutta-NystromIntegrationMethods . . 102 S. Blanes, F. Casas andJ. Ros VIII Table ofContents ConvergenceofFiniteDi?erenceMethodforParabolicProblem withVariableOperator...110 D. Bojovi' c FiniteVolumeDi?erenceSchemefor aSti?EllipticReaction-Di?usionProblemwithaLineInterface ...117 I. A. Braianov Nested-DissectionOrderingsforSparseLUwithPartialPivoting...125 I. Brainman andS. Toledo FractionalStepRunge-ThisvolumeoftheLectureNotesinComputerScienceseriescontainsthep- ceedings of the Second Conference on Numerical Analysis and Applications, which was held at the University of Rousse, Bulgaria, June 11-15,2000.The conferencewasorganizedbytheDepartmentofNumericalAnalysisandStat- ticsattheUniversityofRoussewithsupportfromtheUniversityofSouthern Mississippi, Hattiesburg. The conference was co-sponsored by SIAM (Society for Industrial and Applied Mathematics) and ILAS (International Linear - gebra Society). The o?cial sponsors of the conference were Fujitsu America, Inc. ,Hewlett-PackardGmbH,andSunMicrosystems. Wewouldliketogiveour sincerethankstoallsponsorsandco-sponsorsforthetimelysupport. The second conference continued the tradition of the ?rst one (1996 in Rousse) as a forum, where scientists from leading research groups from the "East" and "West" are provided with the opportunity to meet and exchange ideasandestablishresearchcooperation. Morethan120scientistsfrom31co- triesparticipatedintheconference. Awiderangeofproblemsconcerningrecentachievementsinnumericalan- ysisanditsapplicationsinphysics,chemistry,engineering,andeconomicswere discussed. An extensiveexchangeofideasbetweenscientists whodevelopand studynumericalmethodsandresearcherswhousethemforsolvingreal-lifepr- lemstookplaceduringtheconference. Weareindebtedtoourcolleagueswhohelpedusintheorganizationofthis conference.Wethanktheorganizersofthemini-symposiaforattractingactive andhighlyquali?edresearchers. October2000 LubinVulkov JerzyWa'sniewski PlamenYalamov Table of Contents Numerical Analysis and Its Applications SensitivityAnalysisoftheExpectedAccumulatedReward UsingUniformizationandIRK3Methods ...1 H. Abdallah andM. Hamza SpectralPropertiesofCirculantBandMatricesArisinginODEMethods ...10 P. Amodio AParameterRobustMethodforaProblemwith aSymmetryBoundaryLayer ...18 A. R. Ansari,A. F. HegartyandG. I. Shishkin AnAlgorithmBasedonOrthogonalPolynomialVectors forToeplitzLeastSquaresProblems ...27 M. VanBarel, G. Heinig andP. Kravanja FromSensitivityAnalysistoRandomFloatingPointArithmetics- ApplicationtoSylvesterEquations...35 A. Barraud, S. LesecqandN. Christov ConstructionofSeminumericalSchemes: ApplicationtotheArti?cialSatelliteProblem ...42 R. Barrio StabilityAnalysisofParallelEvaluationofFiniteSeries ofOrthogonalPolynomials ...51 R. Barrio andP. Yalamov OnSolvingLarge-ScaleWeightedLeastSquaresProblems...59 V. Baryamureeba AHybridNewton-GMRESMethodforSolvingNonlinearEquations ...68 S. Bellavia, M. Macconi andB. Morini ComparativeAnalysisofMarchingAlgorithms forSeparableEllipticProblems ...76 G.Bencheva InexactNewtonMethodsandMixedNonlinearComplementaryProblems . . 84 L. Bergamaschi and G. Zilli Skew-CirculantPreconditionersforSystemsofLMF-BasedODECodes ...93 D. Bertaccini andM. K. Ng NewFamiliesofSymplecticRunge-Kutta-NystromIntegrationMethods . . 102 S. Blanes, F. Casas andJ. Ros VIII Table ofContents ConvergenceofFiniteDi?erenceMethodforParabolicProblem withVariableOperator...110 D. Bojovi' c FiniteVolumeDi?erenceSchemefor aSti?EllipticReaction-Di?usionProblemwithaLineInterface ...117 I. A. Braianov Nested-DissectionOrderingsforSparseLUwithPartialPivoting...125 I. Brainman andS. Toledo FractionalStepRunge-KuttaMethodsfortheResolutionof TwoDimensionalTimeDependentCoe?cient Convection-Di?usionProblems...133 B. Bujanda andJ. C. Jorge VariableStepsizesinSymmetricLinearMultistepMethods...144 B. Cano PreliminaryRemarksonMultigridMethodsforCirculantMatrices ...